President Barack Obama said on Monday that Libyan leader Muammar Qadhafi’s regime “is coming to an end” and put the rebels on notice their new government must uphold the democratic ideals that they have professed during six months of U.S. and NATO-backed fighting.

“The situation is still very fluid,” Obama said in remarks from Martha’s Vineyard, Mass., where he is on vacation. “But this much is clear: The Qadhafi regime is coming to an end, and the future of Libya is in the hands of its people.”

Obama’s statement was initially released as an audio recording, but nearly an hour after that came out, the video of Obama’s statement was made public, showing him speaking in a jacket and dress shirt — no tie — in front of a lush backdrop of green trees.

Cautioning that the fighting in Libya is “not yet over” and “there remains a degree of uncertainty and there are still regime elements that pose a threat,” Obama called on Qadhafi to “explicitly” relinquish power. The Libyan leader, the president said, should tell his forces to lay down their arms.

With Qadhafi on his way out, Obama said, what’s important is what comes next.

“As we move forward from this pivotal phase, the opposition should continue to take important steps to take on a transition that’s peaceful, inclusive and just,” the president said, referring to Libya’s Transitional National Council. “As the leadership of the TNC has made clear, the rights of all Libyans must be respected. True justice will not come from reprisals and violence.”

Rather, Obama said, justice “will come from reconciliation and a Libya that allows its citizens to determine their own destiny.”

“In that effort, the United States will be a friend and a partner,” Obama continued. “We will join with allies and partners to continue the work of safeguarding the people of Libya as remaining regime elements menace part of the country, I have directed my team to be in close contact with NATO as well as the United Nations to determine other steps that we can take to deal with the humanitarian impact, we’re working to ensure that critical supplies reach those in need, particularly those who are wounded.”

The president’s remarks came the day after the White House released a three-paragraph statement from him about 10 p.m. ET Sunday. In that statement, Obama said it was clear that “the momentum against the Qadhafi regime has reached a tipping point” and that the Libyan leader of more than four decades should acknowledge that he’s lost his grip on power.

In months of fighting led by NATO, Qadhafi was “cut off from arms and cash, and his forces were steadily degraded” until the regime reached a “tipping point” in recent days, Obama said, repeating the phrase he used Sunday.

The president’s comments on Monday also were aimed at the Libyan people as he told them that their “courage and character have been unbreakable in the face of a tyrant.” He spoke just before sundown in Libya, ahead of what promised to be yet another night of violence mixed with celebrations, as Sunday night was.

“The Libya that you deserve is within your reach,” Obama said. “Going forward, we will stay in close coordination with the TNC to support that outcome. Though there will be huge challenges ahead, the extraordinary events in Libya remind us that fear can give way to hope and that the power of people striving for freedom can bring about a brighter day.”

As Obama spoke, Qadhafi was believed by U.S. officials to still be hiding out in Libya, likely in or near the capital city of Tripoli. At least two of Qadhafi’s sons have been captured by rebel fighters, who have taken control of the vast majority of the capital.

Obama was updated Monday morning by John Brennan, the deputy national security adviser, and planned to talk with his national security team by phone in the afternoon to “discuss Libya and the next steps,” White House spokesman Josh Earnest told reporters at an off-camera briefing.

Meanwhile, Secretary of State Hillary Clinton called the leader of the TNC on Monday and also spoke to leaders from several other countries that have been involved in supporting the rebels.